Algebra and Trigonometry, 2015a

SECTION 2.2 LINEAR EQUATIONS IN ONE VARIABLE 99
Example 16 Finding the Equation of a Line Perpendicular to a Given Line Passing Through a Given Point
Find the equation of the line perpendicular to 5x − 3y + 4 = 0 and passes through the point (−4, 1).
Solution The first step is to write the equation in slope-intercept form.
5x − 3y + 4 = 0
−3y = −5x − 4
y = 5 _
3
x + 4 _
3
We see that the slope is m = 5 _
3
. This means that the slope of the line perpendicular to the given line is the negative
reciprocal, or −
_ 3 . Next, we use the point-slope formula with this new slope and the given point.
5
y − 1 = − 3 _
5
(x − (−4))
y − 1 = − 3 _
5
x − 12 _
5
y = − 3 _
5
x − 12 _
5
+ 5 _
5
y = − 3 _
5
x − 7 _
5
Access these online resources for additional instruction and practice with linear equations.